I Experimental Data - Error in slope

[raniero]

I have conducted a tensile test on five specimens. I intend to do a linear regression for every set of data and get a value for the slope (modulus of elasticity) and its error by finding the standard deviation (using LINEST function on excel) of the slope.

I will now end up with 5 slope values and 5 errors. I will then find the average of 5 slopes, but, how can I find the 'average' of the 5 errors to finally obtain one value for the modulus of elasticity and one error?

Thanks in advance

 

[BvU]

Google weighted average. For the error you have this

 

[raniero]

Google weighted average. For the error you have this

Thanks for your reply. Is this method to combine uncertainties typically used in science experiments ?

 

[Number Nine]

You could do some kind of weighted average, but if you think the slopes are related in such a way that the ""average slope" makes sense, then this really calls for some kind of multilevel model. I recommend looking up (or finding someone in your department familiar with) mixed-effect model.

 

[BvU]

Thanks for your reply. Is this method to combine uncertainties typically used in science experiments ?

Yes. But Number9 has a good point. If your experiments are comparable and your specimens are unsuspect (*), there is no good reason to assume the errors should come out significantly different. Some judgement comes in. Mechanically following the algorithms may not be the best way to go (*) suppose one test strip has a mechanical defect or a slightly different composition -- that would produce an outlier and you simple want to ignore that and average the others - maybe even without weighting.